This is mostly for the late and byzantine army. The Praetorian Guard was effectively gone by this time period, being disbanded by Constantine after he defeated Maxentius in the early 4th century.

The Late Romans did have "special" forces but to the best of my knowledge not "special forces" in the way you're thinking of. Meaning, they had units that were considered elite strike forces, but they were not small units. They were basically the main body army accompanying the emperor.

In the Late Roman army, specifically in the 3rd century with Gallienus, there was a movement away from the the legion system of fairly uniform military units toward a splitting of the army into comitatenses and limitanei, basically they would distinguish the border guard force, which was considered lower quality and mostly there for delaying enemy advances and holding key fortified locations, and then the main strike army, who would actually confront the enemy in the field.

The comitatneses would be the best equipped army, mounted on horseback to ensure a speedy response to threats anywhere in the empire, and be led personally by the emperor (also for political reasons in the 3rd century, as a better equipped army led by someone else would likely result in an overthrow attempt). This practice would continue well into the Byzantine era, with the Opsikion (which is from the latin word obsequium which basically means retinue) which would be the best army in the field under the emperor's direct command, although by then the Byzantines had returned to a sorta levy system similar to the earlier Roman legions. it's just that once again, for political safety reasons, the emperor would keep command of the best troops.

As for special operations, yes there were soldiers for that, but you should understand that our understanding of miltiary special forces, and frankly the military in general, is that of a professional army, with soldiers of a certain training level paid to do this kind of work for the state.

In the Roman era, if you have this body of troops, it was likely under the command of specific renowned general, with specific loyalty to the emperor. I mean in this way, you should consider Belisarius' Gothic troops to be special forces when they helped put down the Nika revolt. They were some of the best trained soldiers available to Justinian, they were personally loyal to Belisarius, who was loyal to the emperor, and they were assigned on a special mission to wipe out everyone in the Hippodrome, something he couldn't trust the main army soldiers to do. .

But you should remember that the main distinction between Roman "special forces" and our "special forces" is that they would consider it "troops who are special" rather than "specially designated special troops."

This would likely apply to the other operations you're considering, reconaissance or harassment, or sabotaging forts. I mean one of my main books of study is a book on "secret" military tactics (bordering on magic military tactics) that include all sorts of crazy battlefield subterfuge worthy of a spy novel, so they were very aware of those tactics (although we dont' know how often they were employed).

The bottom line being, they had soldiers within units who could do such things, but they were known individually, or ad hoc as a group within a military unit who could do such a thing. We have no records of them as a separate special unit.

Maybe this is slightly out side of the original question but as the question said "Roman Military" I'm hopeful it's relevant.

Could someone maybe talk a little about the Varangian Guard in the Eastern Roman Empire and in what regards they could be treated as a "special forces" or not? From what little I know they were maybe more "shock troops" as opposed to "special forces"? Is there any evidence of Varangian Guard members doing "special missions" on behalf of the emperor? Or did the Eastern Roman Empire have any other kinds of special forces?

Part 1

The real answer to this depends on how we define "special forces" or "special operations". Is it a specialized military unit that is focused on a specific strategic outcome? What about tactical outcomes? Or does the definition require the actions to be non-conventional? Regardless, I hope to detail some special and non-combat operations the later Romans of the Late Antique and Medieval periods engaged in.

Gathering intelligence was of the utmost importance for the Romans in this period. With superior intelligence, it was possible to use special operations to wear down, and eventually defeat, superior forces.

To quote the emperor Nicephorus Phocas:

It is imperative first to find out the number of the enemy host and above all what kind of equipment they have, by means of spies, deserters, and prisoners. If the enemy force far outnumbers our own both in cavalry and infantry, avoid a general engagement or close combats and strive to injure the enemy with stratagems and ambushes. The time to seek general engagements with the enemy is when, with the help of God, the enemy has fled once, twice, or three time and are crippled with and fearful, while on the other hand our host is obviously confident

when [The Mother of God] secures Her people's victory for the third time, from that moment on they need not flinch or recoil in fear, be the enemy twice the number of our host.

Modern equivalents to stratagems and ambushes could be carried out by "special forces" but in ancient and medieval times this wasn't quite the case. Different men had different capabilities in addition to their normal duties. For example, a Roman general might form a group from to capture prisoners or perform a night attack but this wouldn't be assigned to the "night attack" special unit so-to-speak, but to a selection of individual soldiers familiar with the local terrain as to not get lost in the darkness.

Now to get into some detail, let's start with intelligence gathering. While the Late Antique Romans and Byzantine Romans used diplomats and envoys to gather intelligence, I will focus on the intelligence gathering mechanisms of the military. First, it was up to local Strategos (governor and general) to post sentries in his territory to watch roads coming from enemy territory and also camp sites. These men had to operate alone in remote areas for weeks at a time to accomplish their tasks effectively. In addition, groups of mounted tasinarioi (light cavalry) should be divided up into small groups and sent into enemy territory to:

charge down on the lands of the enemy, cause harm and ravage them. If possible, they should also capture some of the enemy and bring them back to the commanding general, so that he might obtain information from them about the movement sand plans of the enemy.

Once enemy movements were discovered, the army is to move out to set up defenses along the roads as well as occupying any advantageous positions. For example, hills or cliffs within missile range of the road. In addition to blocking roads, the Romans would also shadow the enemy force. This tactic dates far back in Roman history all the way to the Republic when Quintus Fabius shadowed Hannibal Barca during his campaign in Italy. In the Medieval texts, shadowing is performed by cavalry who are both "experienced and competent" to quote Nicephorus. This special group is to keep the general informed of the enemies movements at all times, so the general can keep his army close enough to strike or ambush the enemy should the circumstances present themselves.

An example of such a circumstance is when the enemy split their forces. If the enemy infantry set up camp while the enemy cavalry go to raid, infantry are to set up ambushes in the towns likely to be raided, and cavalry are to set up ambushes on the roads from the camp to the outlying towns. Like the tasinarioi mentioned earlier, it is the cavalry who are to carry out the more difficult task. In this example to keep the enemy infantry from leaving their camp, and also prevent returning enemy cavalry from entering the camp.

One more example is when the enemy sends out scouts to look for food, water, campsites or event the Roman force, they can be ambushed by combat ready cavalry. Once again we see small groups of cavalry being used to disrupt the enemy on a strategic and tactical level.

The following excerpt from Peri Strategikes illustrates a few points about special operations in this time period well. First, the Byzantine Roman commander has intelligence regarding his enemy's position, and has individuals who has learned the terrain. Second, rather than a specific special forces unit, we see volunteers and experienced men used for the attack. Third, there are a variety of other specialists, such as men to find traps and those who can speak the enemy's language to cause confusion during the attack.

Anyone planning on night operations must first find soldiers who expressly volunteer for this kind of warfare. Both commanders and men should make an agreement under oath. We should swear that when the assignment has been completed, they shall receive their proper rewards. Second, we should seek men who are familiar with the nocturnal security arrangements of the enemy. They should be sure to inform us of all this. In addition, they should know the area in which the enemy are encamped, the road along which we should approach them, so that we should not turn aside on the way.

There should be no moon that night. Otherwise the enemy will observe us marching along. When the sky is clear, while we are still far off choose as a guiding sign the start or stars just above some point or another. By fixing our gaze upon it, we will come upon the enemy's camp by the most direct route. If the sky is cloudy and we cannot see the stars, we should have men who are very well acquainted with the land and with the enemy's camp go on ahead of us. They should have lanterns suspended from their spears. These lanterns should have four sides covered with hides; on three sides the hides should be black, but the fourth white, through which the small lamp can light the way for those walking behind. These men must carry shields covering almost their whole body. They should have iron armor on their lower legs and feet. They should also have iron soles under their feet as protection against caltrops or sharp stakes.

In addition to these, a detachment of soldiers should approach both sides of the enemy's camp. Some should be provided with trumpets and by sounding them frequently they should give the enemy the impression that a large force is attacking them. Others should call out in the enemy's language, presenting themselves as some of their own who are fugitives and urging the others to join them. When the enemy hear them shouting in their own language and believe that they are their own people, some of them will leave the camp behind and follow our men. That side from which the enemy have approached and which leads back to their own country should be left free, so they may have an avenue of escape, for without it, desperation may force them to take their stand all the more bravely.

So far we've been focusing on mostly defensive tactics to be used when the enemy is in Byzantine Roman territory. However, the goals of gathering intelligence, and wearing down the enemy were very important in offensive operations as well. Nicephorus Phocas describes a march into enemy territory:

The commander of the army must first make investigations through spies, prisoners, and deserters and find out the situation of each enemy area, of their villages and fortresses, as well as the size and nature of their cavalry forces. When he is well informed about all these matters, he must take into account the time of year, and he should make incursions and raids with due allowance for the season and the accessibility of the areas.

[while on the march] he should give order to the officers that each of them must detach one hundred or 150 of his light infantrymen and convert them into cavalrymen to accompany the cavalry force…. Similarly, forty or fifty of the kataphraktoi should be set apart, who will leave their heavy armor and that of their horses with the baggage train and head out with the other light horsemen. When the army approaches the enemy region for which it set out, the general guiding the army, or the doukator, must above all be quick and alert to send men out and secure information from prisoners through whom he will acquire accurate knowledge of the region.

It often happens that one or two days before the raid is launched, a body of reinforcements from somewhere else comes to the enemy, while the spies, deserters from the enemy, and captured prisoners coming from the place a week or three to four days previously are unaware of what has happened there one or two days before.

Nikephoros is describing that the light infantry and heavy cavalry (kataphraktoi) are converted into light cavalry to supplement the numbers of light cavalry during the march, bringing the numbers of light cavalry to between half and a third of the total force. While marching through enemy territory, the light cavalry split up into three groups, left, right and center. This formation frequently moves out to raid for provisions, but also prisoners, spies and anyone else that may provide useful information. Once again, it is the cavalry who is carrying out these delicate tasks.

edits for spelling and grammar

This question has been asked before here and got a pretty in-depth answer here by /u/Nick_Gatsby.

Yes, they had the ominously named agentes in rebus (literally--doers of things, which sounds as creepy in Latin as it does in English.) They were more of a secret police than a true force of commandos, but they were well paid and well trained and would be sent on...sensitive...missions. They were under the command of the magister officiorium, so outside of the normal military hierarchy, which made them more reliable for the emperor. As befits a secret unit they are somewhat mysterious to us, but here's an encylopedia entry:

"The agentes in rebus appear to have been set up by Diocletian at the end of the third century ce to replace the corps of frumentarii–imperial couriers and secret policemen – whom he had abolished because of their abuses and unpopularity (Aur. Vict. Caes. 39.44). Like other civil servants of the Late Empire, they wore military uniform and were organized as a military unit, in their case a schola (Not. Dign. (or.) XI.11; (occ.) IX.9), with a hierarchy of cavalry ranks.

They began their career as couriers (Lib. 2.58; 18.135; etc.), and were sometimes referred to as “dispatch riders”(veredarii; CT 8.5.17 (364 ce); Jer. On Abdias 18). They could then progress to overseeing the postal service (cursus publicus), two to each province and known as curagendarii or curiosi (Ct 6.29.1 (355 ce); 2 (357 ce); etc.); Libanius (18.140) called them the “eyes of the emperor.” Eventually, they could be appointed as chiefs of staff (principes officii) to high officials such as provincial governors, frontier commanders (duces; see Dux), Praetorian Prefects (see Praetorian Prefect), and the Prefect of the City. By the fifth century, when they numbered nearly 1,200 (CT 6.27.23), they had come under the overall control of the Master of the Offices (magister officiorum) and were known collectively as magistriani (Ig XIV 949a (p. 694)).

It is clear that they quickly became as unpopular as the frumentarii, often acting as informers and assassins. Constantius II chided them for imprisoning the innocent (CT 6.29.1 (355 ce)), and the emperor Julian (see Julian, emperor remarked that they “know only how to snatch and not to receive” (Amm. Marc. 16.5.11)."

Rankov, B. 2012. Agentes in rebus. The Encyclopedia of Ancient History.

EDIT I'll say another thing, actually, which is that the troops that often served as "commandos" would be the personal bodyguards of generals and emperors; so in Ammianus 16, we find that the general Ursicinus is sent with 10 of his bodyguards on a mission to the rebellious general Silvanus, who has recently declared himself emperor. They're supposed to go and pretend that they don't know that he's done this, and then pretend to swear allegiance to him, and then kill him (they do). This is done by these elite bodyguard troops because they are personally loyal to Ursicinus. More and more in late antiquity generals would surround themselves with personal retinues of soldiers (bucelarii, literally "hard-tack men"), who were not so much soldiers of the state but a private retinue. They were often ethnically non-Roman and could be counted on to have few political opinions. They were excellent for assassinations and also loyal fighters in battle. Especially as the regular army falls apart in the fifth (west) and sixth (east) centuries, we start seeing generals like Belisarius rely more and more on their own bodyguard troops (usually in the hundreds, but occasionally up to a thousand or more) to get the job done when things really need to get done.